Optimal Placement of Controller for Seismic Structures - Design Optimization of Active and Passive Structural Control Systems - page 11

7. Once the stiffness of the fictitious springs is
evaluated, the respective viscous coefficients
can be obtained as:

(1995). The first two are far-field earthquakes,
while the other two are near field earthquakes.
Dynamic time history analyses are performed
to demonstrate the validity of the proposed design
methodology, using four earthquake records rep-
resentative of near field and far field conditions.

T

c =

u

k (24)

1

f

2 π

0

Six Story Building with
Soft Story Behavior

Preliminary design is used to select the size
of the damper unit which will be used during the
optimization process. In the next sessions are
shown the results of preliminary design obtained
for three different buildings.

The building is modeled as a 6 DOF shear type
model with soft story behavior. This type of
behavior is observed in most real buildings that
usually have openings and shops at the first story.
The mass is assumed uniform at all story levels
and equal to m i =3.2×10 4 kg . The lateral stiffness is

NUMERICAL RESULTS

The three integer heuristic approaches presented
in previous paragraphs called SS, WOBI and
ESPS are used to find the optimal location for
dampers. The search methods described can be
applied using the Distinctive Location Strategy and
the Repeated Location Strategy. In the following
numerical examples only the repeated location
strategy is applied. The optimization process
starts with a uniform distribution of the damper
unit (one for each story) which is selected by the
preliminary design. Then the search methods will
re-allocate the dampers 'position. The heuristic
search methods described in previous paragraphs
for optimal location of passive energy dissipation
systems will be investigated numerically for three
different types of buildings: (1) a six story shear
building with soft story behavior; (2) a 10 story
shear building with uniform stiffness through the
story height; (3) a thirty story shear building with
non uniform stiffness through the story height.
(Figure 4). The performance of each search method
for optimizing different objective functions will be
investigated based on four earthquake records that
were selected from a benchmark problem (Ohtori
2004). The earthquakes selected for the analysis
correspond to the earthquake of: El Centro (1940),
Hachinohe (1968), Northridge (1994) and Kobe

k

i =

56 40 10 . ×

3

kN m i = 2 ,  , 6

k 39 48 10 .

3

kN m i 1

= × =

1

and it has been considered for determining the
optimal locations of viscous dampers, by optimiz-
ing the objective functions described in previous
paragraph. The natural periods of the six modes
of the building are: T=0.66, 0.22, 0.13, 0.10, 0.08
and 0.07 sec , and it is assumed a damping ratio
of 5% on the first and the third mode. Dynamic
properties of the building, including the modal
damping ratio and the mass participation factor
are given in Table 4.
The story height considered is h = 3.0 m , the
same in all levels, while the total weight of the
building is 1882.88kN . The structural response in
term of interstory drifts and absolute accelerations
for the uncontrolled structures (unbraced) are
shown in Figure 5.
Preliminary design was performed assuming
25% damping ratio on the first mode assuming
one damper placed at every story unit (uniform
distribution), therefore the fictitious lateral stiff-
ness at a given story is k of =34000 kN/m , while the
equivalent damping coefficient is c o =3588.7
kN*s/m .